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Main concepts
The main concepts of the Global Theory are very simple, as they flow from the fundamental principles of the theory. The first one, Causality, implies that we need two types of objects: events and causal links. Events Basically, events are the fundamental entities between which we observe the causal relationships. However, such a straightforward defintion is not precise enough. Imagine a specific event, say the birth of a child. Looking at it closely, you will soon realize that the definition of this event is not really clear. Is it the moment when the head comes out? What if the feet come first? Or the moment when the body has been completely pulled out of the mother's? What about the umbilical cord? Such a simple example shows that what we use to consider as an event is merely a complex arranging of sub-events. We would then want to further detail those sub-events, following a reductionist approach, only to find out that there is a deeper and more intricated knot of sub-events. We could go on like this until we reach the limits of our knowledge in biological science. However, this ignorance has never prevented us to have children, and to call "birth" the moment of their arrival into the world. This point is very important, since it shows us that even if we cannot precisely define an event, we are able to identify it, to name it and to situate it with respect to other events. According to this logic, we will in this theory regard events as atomic building blocks, even if we know they are made up of sub-events. On the other hand, we could ask ourselves: Where to stop? Isn't any event part of a larger event scheme? How can we talk about a specific event without referring to the broader context it is part of? The answer is that we simply consider events that are relevant for the level of explanation we're looking for. For instance, we won't use particle interactions to explain unemployment rate. Causal links The other fundamental concept is the one of causal link. We say there is such a link from A'' to ''B if A'' causes ''B. Let's have a deeper look at this. If A'' causes ''B, and A'' is the unique cause of ''B, we could actually think of B'' as a natural consequence of ''A. In a sense, B'' is a corollary of ''A: someone causing A'' would implicitly cause ''B. (Think for instance to somebody stabbing somebody else in the chest and leaving him alone in a remote place. Any court would consider him guilty of murder.) This other point is also very important, because it gives us a very simple criterion for defining relevant events: events must have more than one cause. Otherwise, we would consider them as logically equivalent to their cause. It is the interaction between at least two different causes that can generate a new (i.e. logically distinct) event. Duality The two discussions on the basic concepts of the theory lead to an interesting conclusion: events and causal links are interdependant. Events are the entities between which the causal relationships take place, and causal links in turn define what the events are. We could define the causal links as the links between events, or the events as the point of confluence of causal chains. We will elaborate on this concept in the mathematical section. Contribution & relevance When we are analyzing the causal links between a given consequence and their causes, we can think of the contribution of each of these causes. A priori, there is no reason for those contributions to be equal. This is more clear when we consider the links between an event and the causes of their causes. Indeed, let's imagine a ball hitting a wall. The ball after the impact is far more correlated to the ball before the impact than to the wall; the same goes for the wall. Following in the same spirit, we can associate to any list of related events a number that would measure the relevance of this sequence as an explanation for the last event. The contribution to one event to one of its successors is then the sum of the relevances of all paths from this event to this successor (this is very close to the path integral formulation from Richard Feynman, see article in Wikipedia). Threads If we bring this idea a little bit further, we can introduce a derived and very useful concept: the thread. A thread is a sequence of events, with a given relevance. The contribution of an antecedent to a given event is then the sum of the relevances of the threads passing through both events, divided by the sum of the relevances of all threads passing through the event. Actually, it is impossible to isolate a thread completely, since we would have to list an infinity of events. We can only measure the relevance of limited sequences. Moreover, this concept perfectly fits with the previous discussion on the scope of events and links. We can think of threads as woollen threads made from interwoven fibers. On the other hand, it helps structurating the abstraction from one level to the upper. Category:Basics